Recurrent events are prevalent in many longitudinal studies in biomedical and public health settings. A major goal when dealing with recurrent events is to relate the event inter-occurrence times to relevant concomitant variables. Such knowledge provides guidance in formulating public health policies, advocating proper social behavior, determining appropriate medical actions, or dictating courses of action. Aside from the effects of concomitant variables on the event inter-occurrence times, three other aspects need to be considered. First, when the event occurs, an intervention is usually instituted to prolong the reoccurrence of the event. Second, the weakening effect of accumulating event occurrences on the subject needs to be accounted for. Third, since there may be more than one event for a subject, the inter-occurrence times may be affected by unobserved factors, which induce association among these times. A general class of stochastic models which simultaneously incorporate these aspects, and which subsumes many existing specialized intensity models, has been proposed in Pena and Hollander (2002). For this new and general class of models, this project aims (a) to develop and examine appropriate statistical methods for estimating relevant model parameters; (b) to examine the impact of the data accrual aspects of the recurrent event model; (c) to develop methods for validating the model, performing goodness-of-fit tests, and diagnosing the model; and (d) to apply the resulting new statistical methods to real biomedical and public health data sets. The results of this project will provide biomedical and public health practitioners a wide class of stochastic models and new statistical methods appropriate for analyzing recurrent event data arising in public health and biomedical studies such as for instance tumor occurrence, cancer studies, mental health, and many others.